Friday, April 12, 2013

The difference in two squares.

Question:  You have 120 meters of string that you use to make a square that has an area of 900 square meters.   You want to use the 120 meters of string to create a rectangle that is only 500 square meters?  What are the dimensions of the rectangle?

Answer:   The square made with 120 meters of string has four sides of 30 meters each. (30 x 4 =120 and 30 x 30= 900).

This is a classic quadratic equation problem.  We add some string to make the length longer and subtract the same amount of string to make the width shorter

A=(X+K) x (X-K)  = X2 – K2

We know that 900-400 is equal to 500 so k is the square root of 400 or 20.  The dimensions of the rectangle are length of 50 and width of 10.  The sum of the sides of the rectangle 50+50+10+10 is 120.

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